From what I've noticed so far, a ninja's element only influences two parts of the Bond System.

A-What type of bond scroll they use, Earth use Earth Scrolls, Fire uses Fire, etc.

B-The elemental resistance gained, I noticed this when I noticed that I got some nice buffs on some of my people from it, a ninja gives +1% elemental resistance for whatever type they are, so like Jugo, an Earth one, gives +1 earth resistance, at certain intervals

It may be best to use ninja of the opposing type, the type that counters one, if you want to make up for that -20%, or use variety for *l around resistance buff.

At least, this is what I've found while occasionally messing around with the system. There might be more then just that.

But other then all that, it shouldn't change stuff like BP gained or power gained, if it really is just those two things, it just changes what element resistances they gain at certain points. (I think it's every 8? Something around that.)